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Title: Additional note on partial regularity of weak solutions of the Navier-Stokes equations in the class $L^\infty (0,T,L^3(\Omega )^3)$ (English)
Author: Skalák, Zdeněk
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 48
Issue: 2
Year: 2003
Pages: 153-159
Summary lang: English
Category: math
Summary: We present a simplified proof of a theorem proved recently concerning the number of singular points of weak solutions to the Navier-Stokes equations. If a weak solution ${\mathbf u}$ belongs to $L^\infty (0,T,L^3(\Omega )^3)$, then the set of all possible singular points of ${\mathbf u}$ in $\Omega $ is at most finite at every time $t_0\in (0,T)$. (English)
Keyword: Navier-Stokes equations
Keyword: partial regularity
MSC: 35B65
MSC: 35D10
MSC: 35Q10
MSC: 35Q30
MSC: 76D03
MSC: 76D05
idZBL: Zbl 1099.35089
idMR: MR1966346
DOI: 10.1023/A:1026046211510
Date available: 2009-09-22T18:13:05Z
Last updated: 2020-07-02
Stable URL:
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Reference: [4] J. Neustupa: Partial regularity of weak solutions to the Navier-Stokes equations in the class $L^\infty (0,T,L^3(\Omega )^3)$.J. Math. Fluid Mech. 1 (1999), 309–325. MR 1738173, 10.1007/s000210050013
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